Daily Practice · Higher Plus
December 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1993A cuboid measures 4 cm by 10 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd December 1993A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd December 1993A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 4th December 1993A car covers 720 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th December 1993In an algebraic proof, how would you write an odd number in terms of an integer n?
- 6th December 1993y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 7th December 1993A cuboid measures 9 cm by 13 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th December 1993A 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?
- 9th December 1993On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th December 1993Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 11th December 1993Make x the subject of 5x + 8 = y(x + 8).
- 12th December 1993y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 13th December 1993The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 14th December 1993A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 15th December 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 16th December 1993Simplify sqrt(45) + sqrt(125), giving your answer in the form a sqrt(b).
- 17th December 1993Write 6/(x + 3) + 5/(x - 1) as a single fraction.
- 18th December 1993y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 25.
- 19th December 1993In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 20th December 1993The probability of winning a game is 2/5. A player expects 12 wins. How many games did they play?
- 21st December 1993On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd December 1993A rectangle is 22 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd December 1993Solve 3x^2 - 20x + 25 = 0.
- 24th December 1993A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 25th December 1993In a vector proof you find that vector PQ = a - 5b and vector RS = 2a - 10b. What does this show about PQ and RS?
- 26th December 1993A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 27th December 1993A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 28th December 1993Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 29th December 1993f(x) = 8x + 8. Work out the inverse function f^-1(x).
- 30th December 1993y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 31st December 1993A cuboid measures 3 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.