Fourth level block 1 formal homework
- 1. Fourth Level Block 1 Formal Homework 1 1. Calculate: (a) 0.2 x 1.6 (b) 0.255 ÷ 0.5 (c) 1.23 x 0.07 (d) (0.4) 2 – (0.2) 2 2. Lucy and Cameron share £600 in the ratio 2 : 3. Calculate how much each person will receive. 3. Draw a neat 2 times enlargement of this shape. Each box is a 1 centimetre square. 4. Calculate the circumference of this circle. 5. The dimensions of a skeleton model of a cuboid are shown in the diagram below. Find, in its simplest form, an expression for the total length of the edges of the cuboid.
- 2. Fourth Level Block 1 Formal Homework 2 1. Calculate: (a) -6 – (-3) 2 + 10 (b) -12 ÷ (-4) + 7 x (-1)3 (c) 5 2 of 4 1 1 7 3 2 2. Remove the brackets and simplify where possible: (a) 3(a + 2b) (b) 4p(3p – 2q) (c) 2a(4a + 3b) + -7b (d) 5(2x – 6) + 3(8x – 1) 3. Factorise: (a) 7a - 56 (b) 30x – 50y (c) 3v + 4v2 4. Write down the value of a, b and c in the following diagram. 5. Find an expression for the area of the shapes below: (Hint: split this shape first!)
- 3. Fourth Level Block 1 Formal Homework 3 1. Calculate 9 2 of 2 1 2 4 3 4 2. Pot plants cost £20. How many pot plants could be bought with £50? 3. Factorise the following: (a) 3a + 6b (b) 4m2 n – 12mn2 4. Solve these equations to find the value of x: (a) 2(x – 5) = 6 (b) x(x + 3) = x2 - 36 (c) ⅛x + 3 = 28 (d) 3 4 𝑥 + 1 = 1 3 𝑥 − 2 5. Share 350 chocolates between Carol and Mike in the ratio 4:3. 6. The diagram shows a rectangle of length (2n + 3)cm and breadth (n + 1)cm. The perimeter of the rectangle is 44cm. Model this information by means of an equation and solve the equation to find the value of n.
- 4. Fourth Level Block 1 Formal Homework 4 1. Find the answer: (a) -10 + (- 24) (b) -30 + 17 (c) 8 - (-18) (d) (- 9) – (-6) (e) 7 x (-6) (f) (-81) ÷ 9 2. Change the following to scientific notation: (a) 6800 (b) 1 732 000 (c) 0.00049 3. Change the following to a number: (a) 5.12 x 104 (b) 2.3 x 10-6 (c) 4.127 x 10-2 4. Solve each of the following inequations: (a) (b) 5. Donna is buying new kitchen cabinets. She buys : • three Base cabinets of width 50 centimetres • two Wall cabinets of width 30 centimetres • one Drawer cabinet of width 80 centimetres. Calculate the total cost of her kitchen cabinets.
- 5. Fourth Level Block 1 Formal Homework 5 1. 3452 x 13 2. Solve the following equations to find the value of x: 3. Farmer Shaw feeds each of his horses 5 2 of a bale of hay every week. How many bales does he need to feed 12 horses each week? 4. Answer each of the following questions leaving your answers in standard form. (a) Light travels at 1⋅85 × 105 miles per second. How far will it travel in an hour? (b) The speed of light is approximately 299 million metres per second. How far can light travel in a minute? 5. Work out the total area of this shape:
- 6. Fourth Level Block 1 Formal Homework 6 1. Evaluate: (a) 2 x (42 + 2) (b) 81 ÷ 9 + (3 x 4) (c) 2 3 of ( 2 5 + 3 6 ) 2. Write the following in standard form: a) 56,400,000 b) 0.000654 3. Jamie’s garden is in the shape of a right angled triangle. He measured two sides of the garden. Calculate the perimeter of the garden. Round your answer to 1 decimal place. 4. This circular sign has been split into two semi- circles. If the radius of the circle is 12cm, find the area of the shaded part. 5. The annual profit of a company was around £3·2×10 9 during the year 2016. Approximately how much profit did the company make per second?
- 7. Fourth Level Block 1 Formal Homework 7 1. Solve the following equations a) 5(2x – 1) = 45 b) 2(x – 5) – x – 4 = 7 c) 1 2 𝑥 + 1 3 = 4 2. The distance from Neptune to the sun is 4·497× 10 9 km. Write this in normal form. 3. A circle has area 1384·74 square centimetres. Calculate the perimeter of the circle. 4. A ship sails 9km due North and then a further 17km due East. How far is the ship from its starting point? 5. Find the missing angles in the circles below:
- 8. Fourth Level Block 1 Formal Homework 8 3. The results of rolling a dice 100 times are given in this frequency table. Dice value Frequency 1 14 2 16 3 12 4 22 5 20 6 16 What is the mean value of the numbers rolled? 4. Rhombus PQRS has its 2 diagonals, PR and QS, crossing at its centre C. Calculate the perimeter of the rhombus. 1. 2. Factorise: (a) 12t2 + 27t (b) 4xy – 36yz + 20y The circumference of a circle is 9 metres. Find the diameter of the circle.
- 9. 5. Find the length of the missing side x: