6 A rectangular garden measures 38m by 20m, to the nearest metre. Calculate the maximum possible area of the garden.

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1 Year Higher Homework Questions that require the use of a calculator are indicated by a Expand and Simplify ( x + )( x ) A bag contains red balls and blue balls. A ball is picked at random from the bag and not replaced. Another ball is then picked at random. What is the probability that the balls will be the same colour? Simplify 0 Calculate the following (. 0 ) (. 0 ) A rectangular garden measures m by 0m, to the nearest metre. Calculate the maximum possible area of the garden. Solve x + x + = 0. y is directly proportional to the square of x. If y = when x =, find y when x =. 0 y = x x y = x

2 Year Higher Homework Questions that require the use of a calculator are indicated by a Expand and Simplify ( x + )( x + ) A bag contains pink balls and green balls. Hannah picks a ball, at random, from the bag and then doesn t replace it. She then picks another ball at random. What is the probability that she picks a ball of each colour? Simplify Calculate the following (. 0 ) (. 0 ) A rectangular garden measures m by 0m, to the nearest metre. Calculate the minimum possible perimeter of the garden. Simplify y y y is directly proportional to the square of x. If y = when x =, find y when x =.. 0 y = x x y = x +

3 Year Higher Homework Questions that require the use of a calculator are indicated by a Expand and Simplify ( x + )( x + ) A drawer contains socks ( blue and grey). I pick a sock from the draw and don t replace it. I then pick another sock. What is the probability that I pick a blue sock, then a grey sock? Simplify 0 0 Calculate the following ( 0 ) (. 0 ) A rectangular garden measures m by 0m, to the nearest metre. Calculate the maximum possible perimeter of the garden. Simplify, t t p varies directly as the cube of q. When p =, q =, find p when q =. y = x x y = x +

4 Year Higher Homework Questions that require the use of a calculator are indicated by a Expand and Simplify ( x ) Mr Plus picks students at random from his class of students. of his students are boys. What is the probability he picks girls from the class? Simplify + Calculate the following (. 0 ) (. 0 ) An equilateral triangle has sides length cm, measured to the nearest cm. Calculate the maximum possible perimeter of the triangle. Simplify, z + z p varies directly as the cube of q. When p = 000, q =, find q when p =. y = x x + y = x

5 Year Higher Homework Questions that require the use of a calculator are indicated by a Expand and Simplify ( x + ) Three children are chosen at random from a class of boys and girls. Find the probability that no girls are chosen. Simplify Calculate the following (. 0 ) (. 0 ) 0 A regular pentagon has sides. cm, measured to the nearest mm. Work out the minimum possible perimeter of the pentagon. p p Simplify, p p 0. t is directly proportional to the square root of z and t = when z = 00. Find t when z =. y = x x y = x

6 Year Higher Homework Questions that require the use of a calculator are indicated by a 0 Factorise and Solve, x + x = 0 Three children are chosen at random from a class of boys and girls. Find the probability that boys and girl are chosen. Simplify ( + )( + ) Calculate the following (. 0 ) (. 0 ) The number of sweets in a jar is 0, to the nearest 0 sweets. What is the maximum possible amount of sweets in the jar? Simplify, x + x x x x + + x 0. t is directly proportional to the square root of z and t = when z = 00. Find z when t =. x xy = x + y =

7 Year Higher Homework Questions that require the use of a calculator are indicated by a 0 Factorise and Solve, x + x = 0 Three children are chosen at random from a class of boys and girls. Find the probability that a boy is chosen st, a girl nd and then a girl rd. Simplify ( + )( ) Calculate the following (. 0 ) (. 0 ) ( ) A rectangular room measures.m by.m, to the nearest 0 cm. Calculate the maximum possible area of the room. Simplify, y y + 0. p is inversely proportional to q. When p =, q =. What is the value of p when q = x + y = x y =

8 Year Higher Homework Questions that require the use of a calculator are indicated by a Factorise and Solve, x + 0x + = 0 Three cards are selected at random from ten cards labelled to 0. Find the probability that all cards are even numbers. Simplify ( + )( ) Calculate the following (. 0 ) ( 0 ) ( ) A rectangular room measures.m by.m, to the nearest 0 cm. Calculate the maximum possible perimeter of the room. Simplify, s + s + s + s s s is inversely proportional to t. When s =, t =. What is the value of t when s =. Give your answer to significant figures. x y + = x = y x

9 Year Higher Homework Questions that require the use of a calculator are indicated by a 0 Factorise and Solve, x + x = 0 Three cards are chosen at random from ten cards labelled to 0. Find the probability that all the square numbers are chosen. Rationalise the denominator of Calculate the following (. 0 ) (. 0 ) Write in the form a -m A rectangular room measures.m by.m, to the nearest 0 cm. Calculate the minimum possible area of the room. Solve, x = x x + 0. a is inversely proportional to the square of c and when c =, a =. Find the two possible values of c when a =. x + y = x + y =

10 Year Higher Homework 0 Questions that require the use of a calculator are indicated by a Factorise and Solve, x x + = 0 A box contains 0 marbles, five blue, four white and one red. Two marbles are picked at random (neither are replaced). What is the probability that neither marble is blue? Rationalise the denominator of Calculate the following (. 0 ) (. 0 ) Simplify Michael ran a 00 m race in 0 seconds. The time was measured to the nearest second and the distance to the nearest 0 m. Calculate his maximum possible speed in m/s. x + x + Solve, + = Write the following fraction as a recurring decimal h is inversely proportional to the cube of f. It is known that h =. when f =. Find the value of h when f =. 0 x + y = x = y +

11 Year Higher Homework Questions that require the use of a calculator are indicated by a Factorise and Solve, x x + = 0 A box contains 0 marbles, five blue, four white and one red. Two marbles are picked at random (neither are replaced). What is the probability that the marbles are different colours? Rationalise the denominator of Calculate the following (. 0 ) ( 0. 0 ) Simplify p A snail travels a distance of m in minutes. The distance is measured to the nearest cm and the time to the nearest minute. What is the minimum possible speed of the snail? x x + Solve, + = Write the following fraction as a recurring decimal b is inversely proportional to the square of c. When c =, b =. Find values of b and c such that b = c. 0 x + y = x + y =

12 Year Higher Homework Questions that require the use of a calculator are indicated by a Factorise and Solve, x x + = 0 A box contains 0 marbles, five blue, four white and one red. Two marbles are picked at random (neither are replaced). What is the probability that one is red and one is white? Rationalise the denominator of 0 Calculate the following (. 0 ) (. 0 ) m Simplify ( ) Find the maximum possible volume of a cube whose sides are cm, measured to the nearest cm. x x Solve, + = Write the following fraction as a recurring decimal 0 y is inversely proportional to the cube of x, and when x =, y = 0. Find the value of x when y = 0. 0 y = x x y = x +