Daily Practice · Higher Plus
February 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1988 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1988A cuboid measures 14 cm by 13 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd February 1988A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd February 1988On 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?
- 4th February 1988Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 5th February 1988Write 5/(x + 6) + 3/(x - 2) as a single fraction.
- 6th February 1988y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 7th February 1988A cuboid measures 10 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th February 1988A bag holds 5 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th February 1988A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 10th February 1988A rectangle is 8 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th February 1988Solve 2x^2 + 13x + 15 = 0.
- 12th February 1988y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 25.
- 13th February 1988The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 14th February 1988A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 15th February 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th February 1988Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 17th February 1988f(x) = 2x + 8. Work out the inverse function f^-1(x).
- 18th February 1988A train slows steadily from 38 m/s to rest in 8 seconds. Work out its deceleration.
- 19th February 1988In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 20th February 1988The probability of winning a game is 3/4. A player expects 54 wins. How many games did they play?
- 21st February 1988A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 22nd February 1988A block has mass 630 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd February 1988Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 24th February 1988y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 25th February 1988In a vector proof you find that vector PQ = 6a - 3b and vector RS = 30a - 15b. What does this show about PQ and RS?
- 26th February 1988A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 27th February 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th February 1988x = 191 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th February 1988Use the iteration x(n+1) = cube root of (6x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.