Daily Practice · Higher Plus
February 1989 5-a-day
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The batch download puts all 5 tiers' February 1989 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1989A cuboid measures 12 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd February 1989A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd February 1989A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 4th February 1989A car covers 170 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.
- 5th February 1989A quadratic sequence starts 12, 21, 32, 45. Work out the second difference, and the coefficient of n^2.
- 6th February 1989y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 64.
- 7th February 1989The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th February 1989A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 9th February 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th February 1989Rationalise the denominator of 66/sqrt(11), giving your answer in its simplest form.
- 11th February 1989Solve x^2 - 14x + 33 > 0.
- 12th February 1989A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 13th February 1989In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 14th February 1989The probability of winning a game is 3/8. A player expects 39 wins. How many games did they play?
- 15th February 1989A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 16th February 1989Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 17th February 1989Write x^2 + 16x - 15 in the form (x + a)^2 + b.
- 18th February 1989y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 19th February 1989In a vector proof you find that vector PQ = a - b and vector RS = 5a - 5b. What does this show about PQ and RS?
- 20th February 1989A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 21st February 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?
- 22nd February 1989A rectangle is 10 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd February 1989Work out the coordinates of the turning point of y = x^2 + 14x - 15.
- 24th February 1989y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 25th February 1989A cuboid measures 12 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th February 1989A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th February 1989A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 28th February 1989Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).