{"id":34174,"date":"2026-10-23T12:06:56","date_gmt":"2026-10-23T05:06:56","guid":{"rendered":"https:\/\/etest.edu.vn\/?p=34174"},"modified":"2026-10-23T12:06:56","modified_gmt":"2026-10-23T05:06:56","slug":"negative-numbers-la-gi-va-5-bay-so-am-thuong-gap-trong-sat-math","status":"publish","type":"post","link":"https:\/\/etest.edu.vn\/en\/negative-numbers-la-gi-va-5-bay-so-am-thuong-gap-trong-sat-math\/","title":{"rendered":"Negative numbers l\u00e0 g\u00ec v\u00e0 5 b\u1eaby s\u1ed1 \u00e2m th\u01b0\u1eddng g\u1eb7p trong SAT Math"},"content":{"rendered":"

\u0110i\u1ec1u ng\u01b0\u1eddi h\u1ecdc th\u01b0\u1eddng g\u1eb7p<\/b><\/h1>\n

S\u1ed1 \u00e2m kh\u00f4ng ph\u1ea3i l\u00e0 ph\u1ea7n ki\u1ebfn th\u1ee9c qu\u00e1 ph\u1ee9c t\u1ea1p, nh\u01b0ng l\u1ea1i d\u1ec5 khi\u1ebfn h\u1ecdc sinh m\u1ea5t \u0111i\u1ec3m n\u1ebfu t\u00ednh to\u00e1n v\u1ed9i v\u00e0ng ho\u1eb7c b\u1ecf s\u00f3t d\u1ea5u \u1edf m\u1ed9t b\u01b0\u1edbc bi\u1ebfn \u0111\u1ed5i. Ch\u1ec9 m\u1ed9t d\u1ea5u tr\u1eeb sai c\u0169ng c\u00f3 th\u1ec3 d\u1eabn \u0111\u1ebfn k\u1ebft qu\u1ea3 kh\u00f4ng ch\u00ednh x\u00e1c trong c\u00e1c d\u1ea1ng b\u00e0i v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh, tr\u1ecb tuy\u1ec7t \u0111\u1ed1i v\u00e0 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh. B\u00e0i vi\u1ebft n\u00e0y t\u1ed5ng h\u1ee3p nh\u1eefng quy t\u1eafc quan tr\u1ecdng v\u1ec1 s\u1ed1 \u00e2m m\u00e0 h\u1ecdc sinh c\u1ea7n n\u1eafm v\u1eefng \u0111\u1ec3 h\u1ea1n ch\u1ebf sai s\u00f3t v\u00e0 n\u00e2ng cao \u0111\u1ed9 ch\u00ednh x\u00e1c khi l\u00e0m b\u00e0i Digital SAT Math.<\/span><\/p>\n

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Negative numbers l\u00e0 g\u00ec v\u00e0 5 b\u1eaby s\u1ed1 \u00e2m th\u01b0\u1eddng g\u1eb7p trong SAT Math<\/figcaption><\/figure>\n

Negative numbers l\u00e0 g\u00ec?<\/b><\/h1>\n

Negative numbers (s\u1ed1 \u00e2m) l\u00e0 c\u00e1c s\u1ed1 nh\u1ecf h\u01a1n 0, \u0111\u01b0\u1ee3c vi\u1ebft v\u1edbi d\u1ea5u tr\u1eeb ph\u00eda tr\u01b0\u1edbc: \u22121, \u22122,5, \u22123\/4, \u2026 Tr\u00ean tr\u1ee5c s\u1ed1, s\u1ed1 \u00e2m n\u1eb1m b\u00ean tr\u00e1i s\u1ed1 0. S\u1ed1 0 kh\u00f4ng \u00e2m c\u0169ng kh\u00f4ng d\u01b0\u01a1ng.<\/span><\/p>\n

Ch\u00fa \u00fd hai ch\u1eef “nonnegative” v\u00e0 “integer”: \u0111\u1ec1 n\u00f3i “x is an integer” th\u00ec x c\u00f3 th\u1ec3 \u00e2m, v\u00e0 nhi\u1ec1u h\u1ecdc sinh v\u00f4 th\u1ee9c ch\u1ec9 th\u1eed c\u00e1c s\u1ed1 d\u01b0\u01a1ng.<\/span><\/p>\n

S\u1ed1 \u00e2m trong Digital SAT<\/b><\/h1>\n

S\u1ed1 \u00e2m kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t ch\u1ee7 \u0111\u1ec1 \u0111\u1ed9c l\u1eadp trong khung n\u1ed9i dung Digital SAT Math c\u1ee7a College Board, m\u00e0 xu\u1ea5t hi\u1ec7n xuy\u00ean su\u1ed1t nhi\u1ec1u d\u1ea1ng b\u00e0i. H\u1ecdc sinh c\u00f3 th\u1ec3 g\u1eb7p s\u1ed1 \u00e2m khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t (Algebra), l\u00e0m vi\u1ec7c v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai, h\u00e0m s\u1ed1 v\u00e0 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i (Advanced Math), x\u1eed l\u00fd b\u00e0i to\u00e1n v\u1ec1 ph\u1ea7n tr\u0103m gi\u1ea3m (Problem-Solving and Data Analysis) ho\u1eb7c x\u00e1c \u0111\u1ecbnh t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m (Geometry).<\/span><\/p>\n

\u0110\u00e1ng ch\u00fa \u00fd, kho\u1ea3ng 25% c\u00e2u h\u1ecfi SAT Math thu\u1ed9c d\u1ea1ng t\u1ef1 nh\u1eadp \u0111\u00e1p \u00e1n (student-produced response). Theo h\u01b0\u1edbng d\u1eabn c\u1ee7a College Board, d\u1ea1ng c\u00e2u h\u1ecfi n\u00e0y cho ph\u00e9p nh\u1eadp t\u1ed1i \u0111a 5 k\u00fd t\u1ef1 \u0111\u1ed1i v\u1edbi \u0111\u00e1p \u00e1n d\u01b0\u01a1ng v\u00e0 6 k\u00fd t\u1ef1 \u0111\u1ed1i v\u1edbi \u0111\u00e1p \u00e1n \u00e2m, bao g\u1ed3m c\u1ea3 d\u1ea5u tr\u1eeb. \u0110i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 \u0111\u00e1p \u00e1n \u00e2m ho\u00e0n to\u00e0n h\u1ee3p l\u1ec7 n\u1ebfu ph\u00f9 h\u1ee3p v\u1edbi k\u1ebft qu\u1ea3 t\u00ednh to\u00e1n. V\u00ec v\u1eady, khi gi\u1ea3i ra m\u1ed9t s\u1ed1 \u00e2m, h\u1ecdc sinh kh\u00f4ng n\u00ean v\u1ed9i k\u1ebft lu\u1eadn m\u00ecnh l\u00e0m sai m\u00e0 c\u1ea7n ki\u1ec3m tra l\u1ea1i c\u00e1c b\u01b0\u1edbc bi\u1ebfn \u0111\u1ed5i, d\u1ea5u v\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u0111\u1ec1 b\u00e0i.<\/span><\/p>\n

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S\u1ed1 \u00e2m trong Digital SAT<\/figcaption><\/figure>\n

Quy t\u1eafc d\u1ea5u cho 4 ph\u00e9p t\u00ednh<\/b><\/h1>\n

Khi t\u00ednh t\u00edch c\u1ee7a nhi\u1ec1u th\u1eeba s\u1ed1, h\u00e3y x\u00e1c \u0111\u1ecbnh s\u1ed1 l\u01b0\u1ee3ng th\u1eeba s\u1ed1 \u00e2m tr\u01b0\u1edbc khi th\u1ef1c hi\u1ec7n ph\u00e9p nh\u00e2n. N\u1ebfu c\u00f3 s\u1ed1 l\u01b0\u1ee3ng th\u1eeba s\u1ed1 \u00e2m l\u00e0 s\u1ed1 ch\u1eb5n, t\u00edch s\u1ebd mang d\u1ea5u d\u01b0\u01a1ng; ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu c\u00f3 s\u1ed1 l\u01b0\u1ee3ng th\u1eeba s\u1ed1 \u00e2m l\u00e0 s\u1ed1 l\u1ebb, t\u00edch s\u1ebd mang d\u1ea5u \u00e2m. Quy t\u1eafc n\u00e0y gi\u00fap h\u1ecdc sinh x\u00e1c \u0111\u1ecbnh nhanh d\u1ea5u c\u1ee7a k\u1ebft qu\u1ea3 m\u00e0 kh\u00f4ng c\u1ea7n nh\u00e2n l\u1ea7n l\u01b0\u1ee3t t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1, \u0111\u1eb7c bi\u1ec7t h\u1eefu \u00edch khi gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n \u0110\u1ea1i s\u1ed1 trong Digital SAT Math.<\/span><\/p>\n

Lu\u1ef9 th\u1eeba c\u1ee7a s\u1ed1 \u00e2m<\/b><\/h1>\n

Ph\u00e2n bi\u1ec7t (\u22123)\u00b2 = 9 v\u1edbi \u22123\u00b2 = \u22129. \u1ede bi\u1ec3u th\u1ee9c th\u1ee9 hai, lu\u1ef9 th\u1eeba \u0111\u01b0\u1ee3c t\u00ednh tr\u01b0\u1edbc, sau \u0111\u00f3 m\u1edbi l\u1ea5y d\u1ea5u tr\u1eeb.<\/span><\/p>\n

Tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/b><\/h1>\n

Tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ed9t s\u1ed1 l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb s\u1ed1 \u0111\u00f3 \u0111\u1ebfn 0 tr\u00ean tr\u1ee5c s\u1ed1, n\u00ean lu\u00f4n kh\u00f4ng \u00e2m. Ph\u01b0\u01a1ng tr\u00ecnh |A| = c (v\u1edbi c > 0) t\u00e1ch th\u00e0nh hai tr\u01b0\u1eddng h\u1ee3p A = c ho\u1eb7c A = \u2212c. Ph\u01b0\u01a1ng tr\u00ecnh |A| = c v\u1edbi c < 0 v\u00f4 nghi\u1ec7m.\u00a0<\/span><\/p>\n

B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: nh\u00e2n ho\u1eb7c chia cho s\u1ed1 \u00e2m th\u00ec \u0111\u1ed5i chi\u1ec1u<\/b><\/h1>\n

\u0110\u00e2y l\u00e0 quy t\u1eafc b\u1ecb qu\u00ean nhi\u1ec1u nh\u1ea5t. V\u00ed d\u1ee5 2 > 1, nh\u01b0ng nh\u00e2n hai v\u1ebf v\u1edbi \u22121 \u0111\u01b0\u1ee3c \u22122 < \u22121: chi\u1ec1u b\u1ea5t \u0111\u1eb3ng th\u1ee9c ph\u1ea3i \u0111\u1ea3o l\u1ea1i.<\/span><\/p>\n

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B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: nh\u00e2n ho\u1eb7c chia cho s\u1ed1 \u00e2m th\u00ec \u0111\u1ed5i chi\u1ec1u<\/figcaption><\/figure>\n

5 b\u1eaby s\u1ed1 \u00e2m hay g\u1eb7p trong SAT Math<\/b><\/h1>\n
    \n
  1. B\u1ecf ngo\u1eb7c khi thay s\u1ed1 \u00e2m: thay x = \u22123 v\u00e0o x\u00b2 m\u00e0 vi\u1ebft \u22123\u00b2 th\u00ec ra \u22129 thay v\u00ec 9. Lu\u00f4n \u0111\u1eb7t s\u1ed1 \u00e2m trong ngo\u1eb7c khi thay v\u00e0o bi\u1ec3u th\u1ee9c.<\/span><\/li>\n
  2. M\u1ea5t nghi\u1ec7m \u00e2m khi khai c\u0103n: x\u00b2 = 25 c\u00f3 hai nghi\u1ec7m \u00b15, kh\u00f4ng ch\u1ec9 5. Ch\u1ec9 lo\u1ea1i nghi\u1ec7m \u00e2m khi \u0111\u1ec1 c\u00f3 \u0111i\u1ec1u ki\u1ec7n (\u0111\u1ed9 d\u00e0i, s\u1ed1 l\u01b0\u1ee3ng, x > 0, \u2026).<\/span><\/li>\n
  3. Ph\u00e2n ph\u1ed1i d\u1ea5u tr\u1eeb kh\u00f4ng h\u1ebft: \u2212(2x \u2212 7) = \u22122x + 7, kh\u00f4ng ph\u1ea3i \u22122x \u2212 7. L\u1ed7i n\u00e0y hay xu\u1ea5t hi\u1ec7n khi tr\u1eeb hai \u0111a th\u1ee9c v\u00e0 khi \u0111\u1eb7t d\u1ea5u tr\u1eeb ra ngo\u00e0i tr\u01b0\u1edbc l\u00fac ph\u00e2n t\u00edch nh\u00e2n t\u1eed, v\u00ed d\u1ee5 \u2212x\u00b2 + 5x \u2212 6 = \u2212(x\u00b2 \u2212 5x + 6) (xem b\u00e0i “Factoring Quadratic Trinomials”).<\/span><\/li>\n
  4. Hi\u1ec3u sai “gi\u1ea3m” trong b\u00e0i ph\u1ea7n tr\u0103m: gi\u00e1 gi\u1ea3m 20% ngh\u0129a l\u00e0 nh\u00e2n v\u1edbi 0,8, t\u01b0\u01a1ng \u1ee9ng \u0111\u1ed9 thay \u0111\u1ed5i \u221220%. \u0110\u1ec1 h\u1ecfi “percent change” th\u00ec \u0111\u00e1p \u00e1n mang d\u1ea5u \u00e2m, c\u00f2n h\u1ecfi “percent decrease” th\u00ec tr\u1ea3 l\u1eddi 20.<\/span><\/li>\n<\/ol>\n

    C\u00e1ch t\u1ef1 ki\u1ec3m tra khi luy\u1ec7n<\/b><\/h1>\n