Daily Practice · Higher Plus
February 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1992 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1992A car covers 370 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd February 1992Work out the nth term of the quadratic sequence 13, 26, 47, 76, ...
- 3rd February 1992y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 4th February 1992In a vector proof you find that vector PQ = 4a - 2b and vector RS = 20a - 10b. What does this show about PQ and RS?
- 5th February 1992A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th February 1992On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th February 1992Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 8th February 1992The point (2, 5) lies on y = f(x). Write down its image on y = f(x + 3).
- 9th February 1992y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 10th February 1992A cuboid measures 13 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th February 1992A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th February 1992A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 13th February 1992Simplify sqrt(8) + sqrt(8), giving your answer in the form a sqrt(b).
- 14th February 1992Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 15th February 1992y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 81.
- 16th February 1992A cuboid measures 13 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th February 1992A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th February 1992On 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?
- 19th February 1992A rectangle is 14 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th February 1992f(x) = 3x + 7 and g(x) = 5x + 5. Work out fg(-1).
- 21st February 1992A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd February 1992The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 23rd February 1992A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 24th February 1992A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 25th February 1992Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 26th February 1992The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 27th February 1992y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 28th February 1992In 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.
- 29th February 1992The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?