Daily Practice · Higher Plus
October 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1989A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 2nd October 1989A block has mass 240 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd October 1989Make x the subject of 8x + 8 = y(x + 8).
- 4th October 1989y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 36.
- 5th October 1989The 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.
- 6th October 1989A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 7th October 1989On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th October 1989x = 30 and y = 6, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th October 1989Write 3/(x + 4) + 2/(x - 5) as a single fraction.
- 10th October 1989A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 11th October 1989In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 12th October 1989The probability of winning a game is 3/8. A player expects 39 wins. How many games did they play?
- 13th October 1989A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 14th October 1989A car covers 790 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th October 1989Solve 6x^2 + 5x - 4 = 0.
- 16th October 1989y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 17th October 1989In a vector proof you find that vector PQ = 4a + b and vector RS = 20a + 5b. What does this show about PQ and RS?
- 18th October 1989A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 19th October 1989On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th October 1989Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 21st October 1989f(x) = 5x + 5. Work out the inverse function f^-1(x).
- 22nd October 1989y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 23rd October 1989A cuboid measures 15 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th October 1989A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th October 1989A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 26th October 1989Simplify sqrt(50) + sqrt(2), giving your answer in the form a sqrt(b).
- 27th October 1989Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 28th October 1989y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
- 29th October 1989A cuboid measures 13 cm by 4 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th October 1989A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st October 1989On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?