Daily Practice · Higher Plus
February 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1959 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1959f(x) = 8x - 1. Work out the inverse function f^-1(x).
- 2nd February 1959A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd February 1959A cuboid measures 12 cm by 15 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th February 1959A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th February 1959A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 6th February 1959Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 7th February 1959Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 8th February 1959y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 9th February 1959A cuboid measures 10 cm by 14 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th February 1959A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th February 1959On 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?
- 12th February 1959Simplify sqrt(12) + sqrt(12), giving your answer in the form a sqrt(b).
- 13th February 1959Use the iteration x(n+1) = cube root of (3x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 14th February 1959y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 15th February 1959The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 16th February 1959A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 17th February 1959A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 18th February 1959A rectangle is 29 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th February 1959Work out the nth term of the quadratic sequence 0, 7, 18, 33, ...
- 20th February 1959y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 9.
- 21st February 1959In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 22nd February 1959The probability of winning a game is 9/10. A player expects 63 wins. How many games did they play?
- 23rd February 1959On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th February 1959Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 25th February 1959The point (-6, -2) lies on y = f(x). Write down its image on y = f(x - 1).
- 26th February 1959A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 27th February 1959In a vector proof you find that vector PQ = a - 5b and vector RS = 2a - 10b. What does this show about PQ and RS?
- 28th February 1959A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.