Daily Practice · Higher Plus
November 1993 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1993 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1993
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1993A cuboid measures 6 cm by 5 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd November 1993A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd November 1993On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th November 1993Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
- 5th November 1993A quadratic sequence starts 13, 25, 41, 61. Work out the second difference, and the coefficient of n^2.
- 6th November 1993A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 7th November 1993A cuboid measures 12 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th November 1993A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th November 1993A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 10th November 1993A rectangle is 4 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th November 1993Solve x^2 + 6x < 0.
- 12th November 1993y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 13th November 1993The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 14th November 1993A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 15th November 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?
- 16th November 1993Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 17th November 1993Write x^2 - 4x + 10 in the form (x + a)^2 + b.
- 18th November 1993y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 19th November 1993In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th November 1993The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 21st November 1993A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 22nd November 1993A block has mass 370 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd November 1993Work out the coordinates of the turning point of y = x^2 - 16x + 4.
- 24th November 1993y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 36.
- 25th November 1993In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 26th November 1993A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 27th November 1993On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th November 1993x = 104 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th November 1993Simplify (x^2 - x - 42)/(x + 6).
- 30th November 1993A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.