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Form 1 Mathematics Questions and Answers on Integers
Express 1728 and 2025 in terms of their prime factors. Hence evaluate: #(root 3 1728)/( sqrt 2025)#
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1.
Evaluate #(-8÷2+12×9-4×6)/(56÷7×2)#
2.
Evaluate #(28-(-18))/( -2) - (15-(-2)(-6))/(3)#
3.
Evaluate #(-12-:(-3) times 4 -(-20))/(-6 times 6 -: 3 + (-6))#
4.
All prime numbers less than ten are arranged in descending order to form a number (a) Write down the number formed. (b) State the total value of the second digit in the number formed in (a) above.
5.
A square room is covered by a number of whole rectangular slabs of sides 60 cm by 42 cm. Calculate the least possible area of the room in square metres.
6.
(a) Express 10500 in terms of its prime factors (b) Determine the smallest positive number P such that 10500P is a perfect cube.
7.
Three bells ring at intervals of 9 minutes, 15 minutes and 21 minutes. The bells will next ring together at 11.00p.m. Find the time the bells had last rang together.
8.
Evaluate #(22 --14)/(6 times - 2) - (4^2 times -6 - 12)/(72 -: - 8 times 3)#
9.
Ntutu had cows, sheep and goats in his farm. The number of cows was 32 and number of sheep was twelve times the number of cows. The number of goats was 1344 more than the number of sheep. If he sold #3/4# of the goats, find the number of goats that remained.
10.
(a) Evaluate #540\ 396 - 726\ 450 -:3# (b) Write the total value of the digit in the thousands place of the results obtained in (a) above
11.
Given that a = 3 and b =5 and c = #- 1/2#, evaluate #(4a^2 + 2b - 4c)/(1/4(b^2 - 3a)#
12.
The lengths of three wires were 30 m, 36 m and 84 m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained.
13.
Express 1728 and 2025 in terms of their prime factors. Hence evaluate: #(root 3 1728)/( sqrt 2025)#
14.
A retailer bought a bag of tea leaves. If the retailer were to repack the tea leaves into smaller packets of either 40 g, 250 g or 350 g, determine the least mass, in grams, of the tea leaves in the bag.
15.
Without using a calculator, evaluate #(-8 +(-5) times(-8) - (-6))/(-3 +(-8) -: 2 times 4)#
16.
Without using a calculator evaluate, #(-2 (5 + 3) - 9 -: 3 + 5)/(-3 times -5 + -2 times 4)#
17.
A fruit vendor bought 1948 oranges on a Thursday and sold 750 of them on the same day. On Friday, he sold 240 more oranges than on Thursday. On Saturday he bought 560 more oranges. Later that day, he sold all the oranges he had at a price of Ksh 8 each. Calculate the amount of money the vendor obtained from the sales of Saturday.
18.
A number m is formed by writing all the prime numbers between 0 and 10 in an ascending order. Another number n is formed by writing all the square numbers between 0 and 10 in a descending order. (a) Find m-n; (b) Express (m-n) as a product of its prime factors
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