Daily Practice · Higher Plus
January 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1993 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1993A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 2nd January 1993A car covers 840 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd January 1993A quadratic sequence starts 6, 13, 22, 33. Work out the second difference, and the coefficient of n^2.
- 4th January 1993y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 5th January 1993A cuboid measures 5 cm by 8 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th January 1993A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th January 1993On 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?
- 8th January 1993Rationalise the denominator of 33/sqrt(3), giving your answer in its simplest form.
- 9th January 1993Solve x^2 + 9x + 18 > 0.
- 10th January 1993y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 11th January 1993A cuboid measures 12 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th January 1993A bag holds 5 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th January 1993A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 14th January 1993Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 15th January 1993Write x^2 - 2x + 5 in the form (x + a)^2 + b.
- 16th January 1993y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 4.
- 17th January 1993The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 18th January 1993A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 19th January 1993On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th January 1993A rectangle is 6 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st January 1993Work out the coordinates of the turning point of y = x^2 + 16x + 10.
- 22nd January 1993A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd January 1993In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 24th January 1993The probability of winning a game is 3/8. A player expects 15 wins. How many games did they play?
- 25th January 1993A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 26th January 1993Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 27th January 1993Simplify (x^2 + 2x - 3)/(x - 1).
- 28th January 1993y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 29th January 1993In a vector proof you find that vector PQ = 5a - 5b and vector RS = 20a - 20b. What does this show about PQ and RS?
- 30th January 1993A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 31st January 1993On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?