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x, y and z are standard form numbers.
x = 2.5 x 10^{5} y = 3.8 x 10^{4} z = 1.9 x 10^{6}^{
}Calculate:
(a) x - y
(b) x^{2}^{}
^{(c)}
(a) 2.12 x 10^{5} or 212000
(b) 6.25 x 10^{10}^{}
(c) 5000
A magazine contains adverts, photographs and features.
of the pages are adverts and are photographs.
What fraction are features?
There are 24 photographs in a magazine.
The ratio of sports photographs to other photographs is 5:3.
How many sports photographs are there in the magazine?
x 24 = 15
Greg thinks of a positive whole number smaller than 15.
He subtracts 4 from the number and then doubles his result.
He subtracts 4 from the new number and then doubles this result.
He repeats this process several times.
He stops when he gets an answer of 40.
(a) Show that when Greg starts with 12 he
gets an answer of 40.
(b) Find another number that Greg could
have started with to get an answer of 40.
(a) 12 - 4 x 2 = 16
16 - 4 x 2 = 24
24 - 4 x 2 = 40
(b) 10 or 9
Simplify (9 + √7)(9 + √7)
Give your answer in the form a + b√7
81 + 9√7 + 9√7 + √7√7
88 + 18√7
Prove that = 2(1 +√3)
2 + 2√3
2(1 + √3)
A company produces 35 million packets of crisps and snacks each week.
Production is 7 days a week, 24 hours a day.
(a) On average how many packets are
produced in a day? Give your answer in
standard form.
(b) Each packet makes an average profit of
12p. Calculate the average hourly profit
of this company.
(a) 35000000 ÷ 7 = 5000000
5 x 10^{6}^{}
^{}
(b) answer to (a) x 0.12 ÷ 24
25000
Work out the Highest Common Factor (HCF) of 63 and 105
21
The value of a vintage car rises from £36000 to £63000.
Work out the percentage increase in the price of the car.
x100
75%
Evaluate 25^{1/2} x 10^{-2}^{
}^{
}Give your answer as a fraction in its simplest form.
Peter buys a bracelet for £800.
This is a saving of 60% of the original price of the bracelet.
Work out the original price of the bracelet.
40% = 800
800 ÷ 40
2000
Jackson buys 5 rings.
Each ring weighs 34g, to the nearest gram.
What is the least possible total weight of
the five rings.
5 x 33.5 = 167.5
Work out
(3 x 10^{5}) x (4 x 10^{7})
Leave your answer in standard form.
1.2 x 10^{13}
Work out
(4 x 10^{-8}) ÷ (8 x 10^{-2})
Leave your answer in standard form ^{}
5 x 10^{-7}
Work out 4^{1/2} ÷ 6^{-2}
72 and/or -72
50 ÷ 175 x 100 = 28.57% or 28.6%
0.979 seen
9.74 ÷ 0.979 = 9.95 seconds
In a village 35% of the population are female.
60% of the females have blue eyes.
38% of males have blue eyes.
What percentage of the population of the village have blue eyes?
60% of 35%
0.6 x 0.35 = 0.21
38% of 65%
0.38 x 0.65 = 0.247
0.21 + 0.247 = 0.457
45.7%
Express 2008 as a product of its prime factors.
2^{3} x 251
Three friends share a pizza.
of it falls on the floor and is thrown away.
The remainder is shared equally.
What fraction of the whole pizza does each person get?
÷ 3
A pizza costs £6.40.
This is 20% less than its original price.
What was the original price of the pizza?
80% = 6.40
1% = 6.40 ÷ 80
£8
Work out +
What is the value of:
(a) 6^{0}
(b)
(a) 1
(b) 5 or -5
Write down √99 + √44 in the form a√b where a and b are integers.
√99 = 3√11
√44 = 2√11
5√11
a= 5 and b = 11
Work out the Highest Common Factor (HCF) of 42 and 98.
14
James invests £700 for 2 years at 10% per year compound interest. How much interest does he earn?
700 x 1.1^{2} - 700
£147
(a) Write 7200kg in grams.
Give your answer in standard form.
(b) One grain of sand weighs 0.0006g.
Write this number in standard form.