Mock CT3 Paper 2 — Algebraic Fractions, Formulae & Congruency
International Mathematics (0607) — Year 2 / Pre-IGCSE Mock Common Test 3
Created by Miss Clarissa Ng
www.clartutors.com
www.clartutors.com
Instructions: Answer all the questions. All answers should be given in their simplest form. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For π, use your calculator value. A Graphic Display Calculator and/or calculator can be used for this paper. Total: 45 marks.
Syllabus Topics Covered
- Algebraic fractions and simplification
- Making the subject of a formula
- Solutions of quadratic equations (completing the square)
- Graphing quadratic functions using GDC
- Pythagoras' theorem in right-angled triangles
- Congruency of triangles
Section A
Algebraic Manipulation & Formulae
[24 marks]Question 1
The diagram shows a triangle ABC. Find the value of x.
Question 2
Express (
4x
+ 3x−2
) ÷ (2x+1)(x²−2x)
as a single fraction in its simplest form.Question 3
Simplify each of the following. Give your answers in their simplest form.
- (a) (2x + 5)(x − 3)
- (b) (x² + 4x + 4)(x + 2)
- (c) (a² − 9)(a² + 3a)×(a+3)a
(a)
(b)
(c)
Question 4
Make the stated letter the subject of the formula.
- (a) Given that V = πr²h, make r the subject.
- (b) Given that p = 3(x−2)(x+1), make x the subject.
(a)
(b)
Question 5
Without the use of a graphing calculator, solve (2x − 3)² = 49. You must show your working clearly.
Question 6
On the diagram, sketch the graph of y = 2x² + 3x − 5. Indicate the axes intercepts clearly.
- (a) Solve 2x² + 3x − 5 = 0.
- (b) Write down the coordinates of the turning point.
- (c) State the equation of the line of symmetry.
- (d) Find the points of intersection between y = 2x² + 3x − 5 and y = x + 1.
(a)
(b)
(c)
(d)
Question 7
The diagram shows a right-angled triangle with sides (x + 4) cm, (x + 12) cm and (x + 16) cm. The hypotenuse is the longest side.
- (i) By forming an equation in x, show that it reduces to x² − 8x − 48 = 0.
- (ii) Solve the equation x² − 8x − 48 = 0. Give your answers correct to 2 decimal places.
- (iii) Calculate the area of the triangle.
(i)
(ii)
(iii)
Question 8
Some students are planning to buy some pastries for a party. The budget for pastries is $45.
- (a) The price of a muffin is $z. Write down, in terms of z, an expression for the number of muffins the students can buy if they decide to buy muffins only.
- (b) The price of a brownie is $(z + 1). If they spend $45 on muffins only, they can buy 30 more muffins than when they spend $45 on brownies only. Write down an equation in z and show that it simplifies to z² + z − 45 = 0.
- (c) Solve z² + z − 45 = 0. Give your answers correct to 2 decimal places.
(a)
(b)
(c)
Question 9
The diagram shows two triangles, ØABC and ØDEF. All side lengths are given in centimetres.
- (a) State whether the two triangles are congruent. Give a reason for your answer.
- (b) If the triangles are congruent, find the length of side EF.
(a)
(b)
Answer Key
Q1: x = 50 (angles in triangle sum to 180°)
Q2:
(7x−8)(2x+1)
Q3: (a) 2x²−x−15 (b) x+2 (c)
(a−3)a
Q4: (a) r = √(V/πh) (b) x =
(p+6)(3−p)
Q5: 2x−3 = ±7, x = 5 or −2
Q6: (a) x = 1 or −2.5 (b) (−0.75, −6.125) (c) x = −0.75 (d) 2 solutions
Q7: (i) (x+4)²+(x+12)²=(x+16)² → x²−8x−48=0 (ii) x = 12 or −4 (iii) 120 cm²
Q8: (a)
45z
(b) z ≈ 6.12 or −7.12Q9: (a) Yes, SSS congruence (AB=DE=8 cm, AC=DF=10 cm, BC=EF=6 cm) (b) EF = 6 cm