IBMaths: AA SLDPExam Questions1. Number & Algebra1.1 Number Toolkit

Number Toolkit (DP IB Maths: AA SL)

Exam Questions

2 hours19 questions
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Hard
Very Hard
1a
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Let Q =  fraction numerator 30 space sin space 2 a over denominator 8 b end fraction, where a equals 45 degree and b equals 2.

Calculate the exact value of Q.

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1b
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Give your answer from part (a) correct to

(i)
two decimal places

(ii)
two significant figures.

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2a
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Let  R equals fraction numerator 4 x over denominator 6 space cos 5 y end fraction, where x equals 1.25 and y equals 36 degree.

Write the angle of y in radians.

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2b
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Find the value of R. Give your answer as a fraction.

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2c
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Give your answer from part (b) to

(i)
one decimal place

(ii)
three significant figures.

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3a
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Consider the numbers a equals 4.14 cross times 10 to the power of 6 and b equals 2.54 cross times 10 to the power of negative 7 end exponent.

Calculate C space equals space root index 10 of open parentheses a over b close parentheses cubed end root. Give your answer correct to the

(i)
nearest integer

(ii)
three significant figures.

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3b
Sme Calculator2 marks

Give your answer to part (a) (i) in the form a cross times 10 to the power of k, where 1 less or equal than a less or equal than 10 and k element of straight integer numbers.

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4a
Sme Calculator3 marks

A cylinder has radius of 12.7 cm and height of 14.4 cm.

Calculate the volume of the cylinder correct to

(i)
one decimal place

(ii)
three significant figures

(iii)

the nearest integer.

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4b
Sme Calculator2 marks

Write your answer to part (a) (ii) in the form a cross times 10 to the power of k, where 1 less or equal than a less or equal than 10 and k element of straight integer numbers.

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5a
Sme Calculator2 marks

A rectangular field has length, L, of 25.2 m and width, W comma of 21.4 m, each correct to 1 decimal place.

Calculate the lower and upper bound for

(i)
L

(ii)

W

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5b
Sme Calculator4 marks

Calculate the lower and upper bound for the

(i)
perimeter, P
(ii)
area, A comma of the field.

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6
Sme Calculator6 marks

Calculate the following, giving your answer in the form a cross times 10 to the power of k, where 1 less or equal than a less or equal than 10 and k element of straight integer numbers

(i)
4 cross times open parentheses 6.2 space cross times 10 to the power of negative 5 end exponent close parentheses

(ii)

open parentheses 4 space cross times 10 to the power of 5 close parentheses minus open parentheses 5 cross times 10 to the power of 4 close parentheses

(iii)

open parentheses 4321 to the power of negative 1 end exponent close parentheses open parentheses 1.2 cross times 10 to the power of negative 1 end exponent close parentheses

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7a
Sme Calculator2 marks

Consider the following four numbers.

a = 0.272 b = 0.0272 cross times105 c = e(10e)-1 d = 2.72 cross times102

Write down

(i)
the number that is in the form a cross times 10 to the power of k, where 1 less or equal than a less or equal than 10 and k element of straight integer numbers 

(ii)

the largest of these numbers.

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7b
Sme Calculator4 marks
(i)
Find the value of a plus b minus c plus d.

(ii)
Give your answer to part (b)(i) in the form a cross times 10 to the power of k, where 1 less or equal than a less or equal than 10 and k element of straight integer numbers

                      .

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1a
Sme Calculator4 marks

Let P space equals space fraction numerator open parentheses 4 space sin space 2 q minus 2 close parentheses open parentheses 6 space tan space q plus 2 close parentheses over denominator 10 open parentheses r plus s close parentheses squared end fraction, where q equals straight pi over 6, r equals 6 and s equals 2.

Calculate the exact value of P.

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1b
Sme Calculator2 marks

Give your answer from part (a) correct to

(i)
two decimal places.

(ii)
two significant figures.

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2a
Sme Calculator4 marks

Let W space equals space fraction numerator open parentheses 2 cos space 2 x plus y close parentheses open parentheses tan x over 2 minus z close parentheses over denominator 10 open parentheses 5 sin x plus z squared close parentheses end fraction, where x equals straight pi over 2 comma y equals negative 1 and z equals 2.

Find the value of W. Give your answer as a fraction.

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2b
Sme Calculator2 marks

Give your answer from part (a) to

(i)
three decimal places.

(ii)
three significant figures.

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3a
Sme Calculator3 marks

A prism has a cross sectional area of 5.50 cross times 10 cubed space cm squared and volume of 4.40 cross times 10 to the power of 4 space cm cubed.

Calculate the length of the prism.

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3b
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The cross-sectional area of the prism is in the shape of a trapezium and its parallel sides measure 2 m and 2.4 m.

Calculate the height of the trapezium. Give your answer in cm.

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4a
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Mary has found the exact answer for R is  45 over 16.

Write down the exact answer of as a decimal.

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4b
Sme Calculator2 marks

Give your answer from part (a) correct to

(i)
three decimal places

(ii)
one significant figure.

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5a
Sme Calculator2 marks

It is given that sin space a space equals fraction numerator square root of 3 over denominator 2 end fraction and sin space b space equals space 1 half, where  0 less or equal than a less or equal than 90 degree and space 0 less or equal than b less or equal than 90 degree.

Find the size of the angles a and b.

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5b
Sme Calculator4 marks

A circle has radius r equal to square root of fraction numerator sin space a over denominator sin space b end fraction end root space cm.

Find the exact value of the area of the circle, giving your answer in terms of straight pi.

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6a
Sme Calculator1 mark

A medium rare steak should have an internal temperature of 55 degree straight C to 56 degree straight C. Max decides to go to 10 different steak houses, he measures the internal temperature of a medium rare steak at each establishment and records the following:

51.0,   52.1,  62.9,  49.0,  59.8,  50.2,  54.3,  47.7,  48.6,   65.4

Find the mean internal temperature of Max’s recordings.

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6b
Sme Calculator3 marks

Max goes to 5 more steak houses and calculates the mean of all 15 restaurants to be 55.2 degree straight C.

Calculate the mean internal temperature from the 5 additional steak houses Max went to.

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6c
Sme Calculator3 marks

Max records one last steak that has an internal temperature of T degree straight C.

Calculate the interval of T such that the mean internal temperature for all 16 steaks is within the temperature range for a medium rare steak.

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1a
Sme Calculator2 marks

Consider the numbers  a equals 11 square root of 2 comma space b equals left parenthesis 5 plus 6 pi right parenthesis comma space c equals square root of 2 comma space d equals 6 left parenthesis pi minus 1 right parenthesis.

Giving your answer to 1 decimal place, calculate the value of

(i)
a

(ii)
b

(iii)
c

(iv)
d

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1b
Sme Calculator2 marks

Points P and Q have coordinates open parentheses a comma space b close parentheses and open parentheses c comma space d close parentheses respectively.

The formula for the distance, d, between two points with coordinates open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space end subscript y subscript 2 close parentheses is given in your formula booklet.

d equals square root of left parenthesis x subscript 1 minus x subscript 2 right parenthesis squared plus left parenthesis y subscript 1 minus y subscript 2 right parenthesis squared end root

Using your answers from part (a), calculate the distance, d, between points P and Q. Give your answer correct to 1 decimal place.

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2
Sme Calculator5 marks

Let Y equals space open parentheses p q close parentheses to the power of negative 2 end exponent r cubed and T space equals space p q r to the power of negative 1 end exponent, wherespace p equals sin space straight pi over 3, q equals square root of 3, r equals 2.

Find the exact value of YT.

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3a
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Point A has coordinates (minus1, 7) and point B has coordinates (11, 12).

The formula for the distance, d, between two points with coordinates open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is given in your formula booklet.

d space equals space square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared end root


Calculate the distance between points A and B.

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3b
Sme Calculator2 marks

The formula for the coordinates of the midpoint of a line segment with endpoints open parentheses x subscript 1 comma space y subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 close parentheses is given in your formula booklet.

open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma space fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses

Calculate the midpoint of the line segment with endpoints A and B.

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4a
Sme Calculator2 marks

Let S space equals space open parentheses a space sin to the power of 2 space end exponent 4 b close parentheses open parentheses c squared space tan squared space 12 d close parentheses to the power of negative 1 end exponent open parentheses square root of a space plus c minus cos space 48 b close parentheses comma where a = 16, b = 7.5 degree, c = 3 and d = 5 degree

Note: sin2 theta = (sin theta)2

Find the value of S, giving your answer as a fraction.

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4b
Sme Calculator2 marks

Let X = fraction numerator square root of a plus c squared minus 2 s i n space 54 space d over denominator square root of left parenthesis a cubed right parenthesis end root minus a minus c end fraction

Find the value of X comma giving your answer as a fraction.

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4c
Sme Calculator2 marks

Calculate the value of S X comma giving your answer as a fraction.

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5a
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Consider the numbersspace p equals 2.41 cross times 10 to the power of 4 and q equals 4.12 cross times 10 to the power of 5.

Giving your answers in the form a cross times 10 to the power of k comma where 1 less or equal than a less than 10 comma space k element of straight integer numbers comma calculate

(i)
space p plus q

(ii)
space p minus q

(iii)
q minus p

(iv)
p over q

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5b
Sme Calculator2 marks

The formula for the distance, d comma between two points with coordinates left parenthesis x subscript 1 comma space y subscript 1 right parenthesis and open parentheses x subscript 2 comma space y subscript 2 close parentheses is given in your formula booklet.

d equals square root of left parenthesis x subscript 1 minus x subscript 2 right parenthesis squared plus left parenthesis y subscript 1 minus y subscript 2 right parenthesis squared end root

Using your answers to part (a), estimate the distance between points Aleft parenthesis p plus q comma space p minus q right parenthesis  and Bopen parentheses q minus p comma space p over q close parentheses.

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6
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The mean height of the four tallest students in a classroom is 176 cm and the mean height of the six tallest students is 165 cm. The fifth tallest student is 4 cm taller than the sixth tallest student.

Find the heights of the fifth and sixth tallest students.

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