Daily Practice · Higher Plus
February 1997 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1997 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1997In 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.
- 2nd February 1997The probability of winning a game is 9/10. A player expects 72 wins. How many games did they play?
- 3rd February 1997On 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?
- 4th February 1997Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 5th February 1997Use the iteration x(n+1) = cube root of (12x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 6th February 1997y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 7th February 1997In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 8th February 1997A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 9th February 1997A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 10th February 1997A block has mass 730 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th February 1997Work out the nth term of the quadratic sequence 0, 9, 22, 39, ...
- 12th February 1997y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 13th February 1997A cuboid measures 12 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th February 1997A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th February 1997On 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?
- 16th February 1997x = 116 and y = 62, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th February 1997The point (3, -5) lies on y = f(x). Write down its image on y = f(x) + 5.
- 18th February 1997A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 19th February 1997A cuboid measures 7 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th February 1997A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st February 1997A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 22nd February 1997A car covers 630 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.
- 23rd February 1997Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 24th February 1997y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 25th February 1997The 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.
- 26th February 1997A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 27th February 1997On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th February 1997Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.