Daily Practice · Higher Plus
January 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1994A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd January 1994On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd January 1994A block has mass 630 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th January 1994Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 5th January 1994y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 6th January 1994A cuboid measures 7 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th January 1994A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th January 1994A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 9th January 1994x = 184 and y = 168, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th January 1994Use the iteration x(n+1) = cube root of (7x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 11th January 1994y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 36.
- 12th January 1994The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 13th January 1994A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 14th January 1994On 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?
- 15th January 1994A car covers 110 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th January 1994Work out the nth term of the quadratic sequence 11, 26, 49, 80, ...
- 17th January 1994A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 18th January 1994In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 19th January 1994The probability of winning a game is 5/8. A player expects 20 wins. How many games did they play?
- 20th January 1994A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 21st January 1994Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
- 22nd January 1994The point (-3, -4) lies on y = f(x). Write down its image on y = f(x) + 2.
- 23rd January 1994y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 24th January 1994In a vector proof you find that vector PQ = a + 6b and vector RS = 3a + 18b. What does this show about PQ and RS?
- 25th January 1994A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 26th January 1994On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th January 1994Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 28th January 1994Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 29th January 1994y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 30th January 1994A cuboid measures 6 cm by 11 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st January 1994A 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?