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Practice GCSE maths paper

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Subject

Computer Science

264 Documents
Students shared 264 documents in this course
Academic year: 2020/2021
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Mario Pants
The City of Leicester College
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Surname Other names
Candidate Number Centre Number
You must have:
Ruler graduated in centimetres and millimetres, protractor, pair of
compasses, pen, HB pencil, eraser. Tracing paper may be used.
Total
Marks
Write your name here:

MathsBot

@StudyMaths

GCSE (9-1)

Mathematics

Randomly Generated Paper (Non-Calculator)

Higher Topics

4th November 2023
Time: 1 hour 15 minutes
.

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.
You must show all your working.
Diagrams are NOT accurately drawn, unless otherwise indicated.
Calculators may not be used.

Information

The total mark for this paper is 75.
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.
Turn over ►

3.

4.

Find the coordinates of the turning point of f(x) = x²+2x-10.

Work out the coordinates of any intercepts with the coordinate axes.

(Total for Question 3 is 4 marks)

Solve the inequality x² > 10x-24.

(Total for Question 4 is 4 marks)

5.

6.

Here are the first four terms of a Fibonacci sequence:

1, 1, 2, 3, ...

In a Fibonacci sequence, the next term is the sum of the two previous terms.

a) Find the 7th term of this sequence.

The first three terms of a different Fibonacci sequence are a, b, a + b.

b) Show that the 7th term of this sequence is 5a + 8b.

c) Given that the 5th term is 44 and the 7th term is 115, find the value of a and b.

(Total for Question 5 is 6 marks)

Work out the largest integer value of x that satisfies the inequality:

4x-4 < -6x+

(Total for Question 6 is 3 marks)

9.

10.

The line L is a tangent to the circle x 2 + y 2 = 26 at the point (1, 5).

Line L crosses the x-axis at the point P.

Work out the coordinates of P.

(Total for Question 9 is 4 marks)

Here are the first six terms of a Fibonacci sequence:

1, 1, 2, 3, 5, 8, ...

In a Fibonacci sequence, the next term is the sum of the two previous terms.

a) Find the 11th term of this sequence.

The first three terms of a different Fibonacci sequence are e, f, e + f.

b) Show that the 6th term of this sequence is 3e + 5f.

c) Given that the 3rd term is 21 and the 6th term is 89, find the value of e and f.

(Total for Question 10 is 6 marks)

13.

14.

The line L is a tangent to the circle x 2 + y 2 = 128 at the point (8, 8).

Line L crosses the x-axis at the point P.

Work out the coordinates of P.

(Total for Question 13 is 4 marks)

Point A has coordinates (-5, -5).

Point B has coordinates (-3, 5).

Point C has coordinates (-5, -3).

Find an equation of the line that passes through C and is perpendicular to AB.

Give your equation in the form ax + by = c where a and b are integers.

(Total for Question 14 is 4 marks)

15.

16.

Solve the inequality x² ≥ 3x+4.

(Total for Question 15 is 4 marks)

Factorise fully: 150 - 96l².

(Total for Question 16 is 2 marks)

19.

20.

Find the coordinates of the turning point of f(x) = x²-9x+1.

Work out the coordinates of any intercepts with the coordinate axes.

(Total for Question 19 is 4 marks)

Expand: (2x-1)(4x+7)(2x+3)

Give your answer in its simplest form.

(Total for Question 20 is 3 marks)

Question 1 (4 marks)

Gradient from origin to point (1, 1) is 1 ÷ 1 = 1.
Gradient of L is -1 ÷ 1 = -1.
Equation of L is of the form y = -1x + c.
Substituting in (1, 1) gives c = 2.
Equation of L is y = -1x + 2.
When y = 0, x = 2 so P is the point (2, 0).

Question 2 (4 marks)

Gradient from origin to point (8, 4) is 4 ÷ 8 = 0.
Gradient of L is -1 ÷ 0 = -2.
Equation of L is of the form y = -2x + c.
Substituting in (8, 4) gives c = 20.
Equation of L is y = -2x + 20.
When y = 0, x = 10 so P is the point (10, 0).

Question 3 (4 marks)

f(0) = -10, so the graph crosses the f(x) axis at (0,
-10).
Completing the square gives f(x) = (x +1)² -11 so
the coordinates of the turning point (minimum) are
(-1, -11).
The graph crosses the x axis when (x +1)² -11 = 0.
Solving gives x = -1 ±√11.
The graph crosses the x axis at (-1-√11, 0) and
(-1+√11, 0).

Question 4 (4 marks)

Rearranging gives x² -10x +24 > 0.
Factorise to get (x-6)(x-4) > 0.
Therefore x < 4 and x > 6.

Question 5 (6 marks)

Question 11 (3 marks)

Expanding and simplyfying the first two pairs of
brackets gives:
(16x²-8x-63)(x-10).
Now expand and simplify to get:
16x³-168x²+17x+630.

Question 12 (2 marks)

20q² - 80r² = 5(4q² - 16r²)
Factorising using difference of two squares gives:
5(2q + 4r)(2q - 4r).

Question 13 (4 marks)

Gradient from origin to point (8, 8) is 8 ÷ 8 = 1.
Gradient of L is -1 ÷ 1 = -1.
Equation of L is of the form y = -1x + c.
Substituting in (8, 8) gives c = 16.
Equation of L is y = -1x + 16.
When y = 0, x = 16 so P is the point (16, 0).

Question 14 (4 marks)

Gradient of AB is 10 ÷ 2 = 5.
Gradient of line perpendicular to AB is -1/ 5.
Equation of perpendicular is of the form y = -1/ 5 x +
c
At the point C, (-3) = -1/ 5 (-5) + c.
c = -4.
x + 5y = -20.

Question 15 (4 marks)

Rearranging gives x² -3x -4 ≥ 0.
Factorise to get (x-4)(x+1) ≥ 0.
Therefore x ≤ -1 and x ≥ 4.

Mark Scheme - Total Marks: 75

Equation of L is of the form y = -0 + c.
Substituting in (1, 5) gives c = 5.
Equation of L is y = -0 + 5.
When y = 0, x = 26 so P is the point (26, 0).

Question 10 (6 marks)

a) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
1st term is 1e + 0f
2nd term is 0e + 1f
3nd term is 1e + 1f
4rd term is 1e + 2f
5th term is 2e + 3f
6th term is 3e + 5f
c) We have a pair a simultaneous equations:
1e + 1f = 21
3e + 5f = 89
Solving these gives e = 8 and f = 13

Question 20 (3 marks)

Expanding and simplyfying the first two pairs of
brackets gives:
(8x²+10x-7)(2x+3).
Now expand and simplify to get:
16x³+44x²+16x-21.
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Practice GCSE maths paper

Subject: Computer Science

264 Documents
Students shared 264 documents in this course
Degree • Grade:

Sixth Form (A Levels)

• A2 - A Level
Was this document helpful?
04/11/2023, 20:30
Practice GCSE maths paper
https://mathsbot.com/practicePaper
1/16
Surname Other names
Centre NumberCandidate Number
You must have:
Ruler graduated in centimetres and millimetres, protractor, pair of
compasses, pen, HB pencil, eraser. Tracing paper may be used.
Total
Marks
Write your name here:
MathsBot.com
@StudyMaths
GCSE (9-1)
Mathematics
Randomly Generated Paper (Non-Calculator)
Higher Topics
.
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.
You must show all your working.
Diagrams are NOT accurately drawn, unless otherwise indicated.
Calculators may not be used.
Information
The total mark for this paper is 75.
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.

Students also viewed

Related documents