Mock CT3 Paper 1 — Algebraic Fractions, Formulae & Quadratics
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 (factorisation)
- Graphing quadratic functions using GDC
- Pythagoras' theorem in real-life contexts
Section A
Algebraic Manipulation & Formulae
[26 marks]Question 1
Simplify each of the following. Give your answers in their simplest form.
- (a) 4m²n6mn2
- (b) (3x²y)29xy3
- (c) 2a3b + 6ab24ab
(a)
(b)
(c)
Question 2
Express each of the following as a single fraction in its simplest form.
- (a) 3b+1+2b−1
- (b) (xy−yx) ÷x+yxy
(a)
(b)
Question 3
Make the stated letter the subject of the formula.
- (a) Given that km+2=13m−1, make m the subject.
- (b) Given that T = 2π√(l/g), make l the subject.
(a)
(b)
Question 4
Without the use of GDC, solve each of the following equations.
- (a) 3(x−2)(x+5) = 0
- (b) x² + 7x + 12 = 0
(a)
(b)
Question 5
The diagram shows a vertical flagpole AB standing on horizontal ground. A person stands at point C, 12 m from B. The person's eye level is 1.6 m above the ground. The distance from the person's eye to the top of the flagpole is 20 m.
Find the height of the flagpole.
Question 6
On the diagram, sketch the graph of y = x² − 4x − 5. Indicate the axes intercepts clearly.
- (a) Solve x² − 4x − 5 = 0.
- (b) Write down the coordinates of the turning point.
- (c) State the equation of the line of symmetry.
(a)
(b)
(c)
Question 7
A farmer buys a number of sheep for $1,200.
- (a) Given that each sheep costs $y, write down an expression, in terms of y, for the number of sheep he bought.
- (b) The price of each sheep was decreased by $4. Write down an expression, in terms of y, for the number of sheep he can now buy.
- (c) He can buy 6 more sheep when the price is decreased by $4. Show that y² − 4y − 480 = 0.
- (d) Solve the equation y² − 4y − 480 = 0.
- (e) Find the number of sheep he bought at the original price.
(a)
(b)
(c)
(d)
(e)
Answer Key
Q1: (a)
2m3n
(b) x³9y2
Q2: (a)
(5b+1)(b²−1)
(b) (x−y)x
Q3: (a) m =
(k+1)(3k−1)
Q4: (a) x = 2 or −5 (b) x = −3 or −4
Q5: 16.8 m
Q6: (a) x = 5 or −1 (b) (2, −9) (c) x = 2
Q7: (a)
1200y
(b) 1200(y−4)