Non calculator starter questions

1.Evaluate . 2K

2.Evaluate . 2K

3.Solve the inequality , where x is a whole number.

4K

4.Evaluate when . 2K

5.(a)Factorise . 2K

(b)Hence, simplify the fraction . 2K

6.(a) Express as a single fraction in its simplest form .

3K

(b) Change the subject of the formula to H in 2K

7.Evaluate . 2K

8. Evaluate: of . 2K

9The function is given by the formula , where x is a real number.

(a)Find the value of 2K

(b)Find the values of a for which . 3K

10.Solve the equation , where x is a real number. 3K

11.The median of five consecutive even integers is .

(a) Write down, in terms of p , expressions for the five integers. 2K

(b) Show that the mean can be expressed as . 2K

12.Evaluate . 2K

13.Evaluate . 2K

14.Solve the inequality, where x is a whole number. 4K

15.Given that , change the subject of the formula to Q. 2K

16.Factorise:. 3K

17. A function f is defined on the set of integers by the formula:

Given that , find 3R

18.(a)Simplify. 2K

(b)Evaluate. 2K

19.(a)Solve the equation 3K

(b)Multiply out the brackets and simplify your answer

3K

20.Evaluate: 83 – 135 ÷ 5.2K

21.Evaluate:.2K

22.Change the subject of the formula: to P.3K

23.Solve the inequality:

4K

24.Expressas a single fraction.2K

25.Evaluate 2K

26.Work out the answer to 2K

27.

(a)Find . 2K

(b)If and , find the possible value(s) for a.3K

28.Solve the equation

.3K

29.(a)Factorise fully. 2K

(b)Hence simplify. 2K

Miscellaneous

1.To make one “Double Decker” chicken sandwich

3 slices of bread and 2 pieces of chicken are used.

The chef at the café has 42 slices of bread and 18

pieces of chicken in his kitchen.

What is the maximum number of ‘Double Decker’ chicken sandwiches that

the chef can make?3R

2.The cost of having a booklet printed by ‘TRUEPRINT’ depends on the number of

pages and the number of booklets to be printed.

The details are shown in the table below.

NUMBER of PAGES / COSTS
Less than or equal to 2
Greater than 2 pages but less than or equal to
6 pages.
Greater than 6 pages / £015 for each of the first 300 booklets printed
£021 for each of the first 300 booklets printed
£029 for each of the first 300 booklets printed
Where the number of booklets to be printed at any one time is greater than 300 a charge of £012 is made for each additional booklet (for any number of pages).

(a)Calculate the cost of printing 450 booklets with 4 pages in each.2R

(b)Show clearly that the formula for the cost, £C, of having b booklets

printed, where b is greater than 300 and each booklet consists of 4 pages, can be

written as

3R

13.Here are the first 6 rows of a pattern. The pattern is known as Pascal’s Triangle.

The numbers in the next row are found from the numbers in the previous row,

as shown below,

(a)Write down the numbers in the 7th row of Pascal’s triangle. 1R

Pascal’s triangle can be used as a method of expanding brackets without

multiplying them out:

(b) The expansion of (x+ y) 4 is 1x4 + 4x3y1 + 6x2y2 + 4x1y3 + 1y4

Write down the expansion of (x+ y) 5 3R

14.The Golden Rectangle is a unique and very important shape in Maths. The special

propertyof the Golden Rectangle is that the ratio of its length to its width is

approximately 162.

Golden Ratio =

Leonardo de Vinci painted many of his masterpieces on Golden rectangle canvases,

The Mona Lisa being one of his most famous.

The length of the canvas used to for The Mona Lisa was 729cm.

Use the above information to calculate the approximate area of this canvas. 3R