Mathematics

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Mathematics

2022 Paper 1 (Non-Calculator) Higher Tier

Time: 1 hour 30 minutes

You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser.

Total Marks

Instructions

? Use black ink or ball-point pen. ? Fill in the boxes at the top of this page with your name, centre number and candidate number. ? Answer all questions. ? Answer the questions in the spaces provided ? there may be more space than you need. ? Calculators may not be used. ? Diagrams are NOT accurately drawn, unless otherwise indicated. ? You must show all your working out.

Information

? The total mark for this paper is 80 ? The marks for each question are shown in brackets ? use this as a guide as to how much time to spend on each question.

Advice

? Read each question carefully before you start to answer it. ? Keep an eye on the time. ? Try to answer every question. ? Check your answers if you have time at the end.

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Higher Tier Formulae Sheet

Perimeter, area and volume

Quadratic formula

Where a and b are the lengths of the parallel sides and h is their perpendicular separation:

Area of a trapezium =

1 2

(a

+

b)

h

Volume of a prism = area of cross section ? length

The solution of ax2 + bx + c = 0

where a 0

x

=

- b? b2 -4

2a

ac

Where r is the radius and d is the diameter:

Circumference of a circle = 2r = d

Area of a circle = r2

Pythagoras' Theorem and Trigonometry

In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:

c a

a2 + b2 = c2

In any right-angled triangle ABC where a, b and c are the length of the sides and c is the hypotenuse:

A b

C

sin

A=

a c

cos

A=

b c

tan

A=

a b

In any triangle ABC where a, b and c are the length of the sides:

b

a

sine rule:

a sin A

=

b sin B

=

c sin

C

cosine rule: a2 = b2 + c2 ? 2bc cos A

A

c

B

Area of triangle =

1 2

ab sin C

Compound Interest

Where P is the principal amount, r is the interest rate over a given period and n is number of times that the interest is compounded:

( ) Total accrued = P

1

+

r 100

n

Probability

Where P (A) is the probability of outcome A and P (B) is the probability of outcome B:

P (A or B) = P (A) + P (B) ? P (A and B)

P (A and B) = P (A given B) P(B)

END OF EXAM AID

1 Write 240 as a product of its prime factors.

2

(a) Work out

37 4 - 10

(Total for Question 1 is 2 marks)

(2)

(b) Work out

2

1 3

?

3 5

Give your answer as a mixed number in its simplest form.

(2) (Total for Question 2 is 4 marks)

3

In a bag there are only red counters, blue counters, green counters and yellow counters.

A counter is taken at random from the bag.

The table shows the probabilities that the counter will be green or will be yellow.

Colour

Red

Probability

Blue

Green

Yellow

0.35

0.20

The probability that the counter will be red is twice the probability that the counter will be blue. There are 21 green counters in the bag. Work out the number of red counters in the bag.

(Total for Question 3 is 4 marks)

4

Here is the graph of y = 2x + 6 ? x2

y 8

6

4

2

-6

-4

-2

O

-2

2

4

6x

-4

-6

(a) Write down the turning point of the graph y = 2x + 6 ? x2

(b) Use the graph to find the roots of the equation x2 = 2x + 6

(................... , ...................) (1)

.......................................................... (2)

(Total for Question 4 is 3 marks)

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................

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