Daily Practice · Higher Plus
February 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1993 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1993A block has mass 500 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd February 1993In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 3rd February 1993y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 4th February 1993A cuboid measures 4 cm by 5 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th February 1993A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th February 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 7th February 1993x = 105 and y = 88, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th February 1993Make x the subject of 7x + 2 = y(x + 2).
- 9th February 1993y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 36.
- 10th February 1993A cuboid measures 13 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th February 1993A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th February 1993On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th February 1993A car covers 400 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.
- 14th February 1993Write 6/(x + 6) + 2/(x - 3) as a single fraction.
- 15th February 1993A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
- 16th February 1993The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 17th February 1993A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 18th February 1993A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 19th February 1993Rationalise the denominator of 30/sqrt(5), giving your answer in its simplest form.
- 20th February 1993Solve 10x^2 - 19x - 15 = 0.
- 21st February 1993y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 22nd February 1993In 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.
- 23rd February 1993The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 24th February 1993On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th February 1993Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 26th February 1993f(x) = 5x + 1. Work out the inverse function f^-1(x).
- 27th February 1993y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 28th February 1993In a vector proof you find that vector PQ = 5a - 2b and vector RS = 10a - 4b. What does this show about PQ and RS?