Daily Practice · Higher Plus
October 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2002f(x) = 5x - 5 and g(x) = 4x + 5. Work out fg(4).
- 2nd October 2002y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 3rd October 2002In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 4th October 2002The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 5th October 2002A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 6th October 2002x = 153 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th October 2002The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 8th October 2002y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 81.
- 9th October 2002In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 10th October 2002A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 11th October 2002On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th October 2002A car covers 120 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th October 2002A quadratic sequence starts 13, 28, 53, 88. Work out the second difference, and the coefficient of n^2.
- 14th October 2002A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 15th October 2002A cuboid measures 13 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th October 2002A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th October 2002A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 18th October 2002Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 19th October 2002Solve x^2 - 4x - 5 < 0.
- 20th October 2002y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 21st October 2002A cuboid measures 11 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd October 2002A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd October 2002On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th October 2002Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 25th October 2002Write x^2 - 16x + 9 in the form (x + a)^2 + b.
- 26th October 2002y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 27th October 2002The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 28th October 2002A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 29th October 2002A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 30th October 2002A rectangle is 22 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st October 2002Work out the coordinates of the turning point of y = x^2 - 16x + 14.