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Sir Chiwanza

This document is a revision test for real numbers, dated 01/03/25, with a total of 70 marks. It includes various mathematical problems such as solving quadratic equations, simplifying fractions, and working with inequalities. The test covers a range of topics including geometry, percentages, population calculations, and logarithmic equations.

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Edison Chiwanza
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34 views2 pages

Sir Chiwanza

This document is a revision test for real numbers, dated 01/03/25, with a total of 70 marks. It includes various mathematical problems such as solving quadratic equations, simplifying fractions, and working with inequalities. The test covers a range of topics including geometry, percentages, population calculations, and logarithmic equations.

Uploaded by

Edison Chiwanza
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SIR

SIR-EDDIE
REAL NUMBERS REVISION TEST
DATE 01/03/25
TOTAL MARKS 70

ANSWER ALL QUESTIONS


1a) The solution of a quadratic equation are 𝑥 = −1 and 𝑥 = 3. Write down the quadratic equation
in the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 where 𝑎, 𝑏 and 𝑐 are integers.
[3]
1 1
b) Express 𝑥−2 + 𝑥+1 as a single fraction in its simplest form. Hence or otherwise, solve the equation
1 1 3
𝑥−2
+ 𝑥+1 = 𝑥. [4]

2a. Given that 2𝑥 + 𝑦 = 10, solve the equations

4𝑥 2 − 𝑦 2 = 40
2𝑥 + 𝑦 = 10 [3]
1 2 9
b) Solve the equation (𝑦 + ) = [3]
4 16

𝑣−𝑢 2
3a) Express (𝑢−𝑣)2 − as a single fraction in its simplest form. [3]
𝑣−𝑢

𝑚2 −𝑚−12
b) Simplify 𝑚3 −9𝑚
[3]
3𝑎 3𝑏
c) Express 2𝑎−𝑏 + 2𝑏−4𝑎 as a single fraction in its simplest form. [3]

4. A rectangle is 9,1 cm long and 5,7 cm wide correct to one decimal place.

a) State the least possible width of the rectangle. [1]

b) Find the limits within which the perimeter of the rectangle lies. [2]

c) Express 2046.489 correct to

i) the nearest ten. [1]

ii) 2 decimal place [1]

iii) 2 significant figures. [1]


371+849
d) By correcting each number to 1 significant figure, estimate the value of . [3]
√668−643

TYPED BY SIR EDDIE & SANCHO


5. Express 1 hectare as a percentage of 0.25𝑘𝑚2 . [2]

6a. i) Solve the inequality 5𝑥 − 6 < 2𝑥 − 3 ≤ 3𝑥 + 1, giving your answer in the form 𝑎 ≤ 𝑥 < 𝑏,
where 𝑎 and 𝑏 are integers.

ii) Illustrate the solution on the a number line. [5]

b) Solve the inequality 𝑦 − 4 < 3𝑦 + 2 ≤ 6 − 𝑦. Hence list the integral values of 𝑦 that satisfy the
inequality. [4]

7a) Simplify the following, giving your answer in standard form.

i) √6250000 [2]

ii) 5−2 [2]

b) The population of town A is 4.5 × 104 and that of town B is 3.9 × 104.

i) Calculate the difference the two populations. [1]

ii) The population of town A is 125% greater than what is was forty years ago. Calculate the
population of town A forty years ago. Give the answer in standard form. [2]

8a) Find 𝑝 in base eight such that 𝑝8 + 2345 = 4215 [3]

b) If 1203 = 13𝑛 + 10𝑛 , find the value of 𝑛. [3]

c) Express 52 + 3 × 5 + 4 as a number in

i) base 5. [1]

ii) base 8. [2]

9ai) Show that 2𝑙𝑜𝑔5 (3𝑥 + 2) − 𝑙𝑜𝑔5 2 = 1 reduces to 3𝑥 2 + 4𝑥 − 2 = 0.

ii) Solve the equation 3𝑥 2 + 4𝑥 − 2 = 0, giving your answer to two decimal places. [9]

b) Express 𝑙𝑜𝑔10 𝑥 − 2𝑙𝑜𝑔10 𝑦 = 1 as an equation index form. [3]

TYPED BY SIR EDDIE & SANCHO

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